On the co-derivative of normal cone mappings to inequality systems
Authors
- Henrion, René
ORCID: 0000-0001-5572-7213 - Outrata, Jiří
- Surowiec, Thomas
ORCID: 0000-0003-2473-4984
2010 Mathematics Subject Classification
- 90C30 49J53
Keywords
- Mordukhovich co-derivative, normal cone mapping, calmness
DOI
Abstract
The paper deals with co-derivative formulae for normal cone mappings to smooth inequality systems. Both, the regular (Linear Independence Constraint Qualification satisfied) and nonregular (Mangasarian-Fromovitz Constraint Qualification satisfied) case are considered. A major part of the results relies on general transformation formulae previously obtained by Mordukhovich and Outrata. This allows to derive exact formulae for general smooth, regular and polyhedral, possibly nonregular systems. In the nonregular, nonpolyhedral case a generalized transformation formula by Mordukhovich and Outrata applies, however a major difficulty consists in checking a calmness condition of a certain multivalued mapping. The paper provides a translation of this condition in terms of much easier to verify constraint qualifications. A series of examples illustrates the use and comparison of the presented formulae.
Appeared in
- Nonlinear Anal., 71 (2009) pp. 1213-1226
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